Advertisements
Advertisements
Question
The cylindrical tube of a spray pump has a cross-section of 8.0 cm2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min–1, what is the speed of ejection of the liquid through the holes?
Solution 1
Total cross-sectional area of 40 holes, `a_2`
`= 40 xx 22/7 xx (1xx10^(-3))^2/4 m^2`
`= 22/7 xx 10^(-5) m^2`
Cross-sectional area of tube, `a_1 = 8 xx 10^(-4) m^2`
Speed inside the tube,. `v_1 = 1.5 m min^(-1) = 1.5/60 ms^(-1)`
Speed of ejection, `v_2 = ?`
Using `a_2v_2 = a_1v_1`
We get
` v_2 = (a_1v_1)/a_2 = (8xx10^(-4) xx (1.5/60) xx 7)/(22xx10^(-5)) ms^(-1) = 0.64 ms^(-1)`
Solution 2
Area of cross-section of the spray pump, A1 = 8 cm2 = 8 × 10–4 m2
Number of holes, n = 40`
Diameter of each hole, d = 1 mm = 1 × 10–3 m
Radius of each hole, r = d/2 = 0.5 × 10–3 m
Area of cross-section of each hole, a = πr2 = π (0.5 × 10–3)2 m2
Total area of 40 holes, A2 = n × a
= 40 × π (0.5 × 10–3)2 m2
= 31.41 × 10–6 m2
Speed of flow of liquid inside the tube, V1 = 1.5 m/min = 0.025 m/s
Speed of ejection of liquid through the holes = V2
According to the law of continuity, we have:
`A_1V_1 = A_2V_2`
`V_2 = (A_1V_1)/A_2`
`= (8xx10^(-4)xx0.025)/(31.61xx10^(-6))`
`= 0.633 m/s`
Therefore, the speed of ejection of the liquid through the holes is 0.633 m/s
APPEARS IN
RELATED QUESTIONS
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s–1and 63 m s–1 respectively. What is the lift on the wing if its area is 2.5 m2? Take the density of air to be 1.3 kg m–3.
Figures (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?
In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.
Suppose the tube in the previous problem is kept vertical with A upward but the other conditions remain the same. the separation between the cross sections at A and B is 15/16 cm. Repeat parts (a), (b) and (c) of the previous problem. Take g = 10 m/s2.
What is the basis of Bernoulli’s principle?
A large number of liquid drops each of radius 'a' are merged to form a single spherical drop of radius 'b'. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is [p = density of liquid, T = surface tension of liquid] ____________.
Dynamic lift caused by spinning is called ______.
The working of venturimeter is based on ______.
If p0 = 1.03 × 105 Nm–2, ρ0 = 1.29 kg m–3 and g = 9.8 ms–2, at what height will the pressure drop to (1/10) the value at the surface of the earth?
Calculate the velocity with which the liquid gushes out of the 4 cm2 outlet, if the liquid flowing in the tube is water and the liquid in the U tube has a specificity 12. The velocity of the liquid at point A is `sqrt20.2` m/s ______.
